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Make a continuous map cut out?

I'm working an an equi-rectangular projection of an overworld map. I'm using Photoshop CS6. I'm just wondering how to make the map edges line up so that if I make a different projection of it using whatever program, there isn't a line of inconsistency where the left and right edges of the map meet. I think this also affects the top and bottom as well. Is there any simple way to make sure that the two edges line up properly and seamlessly? Or do I need to iron out the inconsistencies by hand?

best thing is to temporarily) copy/paste a thin part of the left/right-most part of the map and drag it to the other edge and use it as a reference for plotting the coastlines there.

the poles are more difficult due to the amount of distortion there there's a lot of back/forth involved in making sure the coastlines look right in other projections. the best thing (that i know of) is to use the NASA G. projector for this http://www.giss.nasa.gov/tools/gprojector/ (though link is giging me a 403 error - ?)

Alright, that makes sense for getting coastlines to line up. The little sliver technique. What if I want to make a randomized texture for the ocean? Anyway to do that and make sure the edges connect seamlessly?

Textures aren't going to survive reprojection anyway. Keep your symbology simple and don't waste time on decoration or careful label placement until you have the map in its final projection.

Making the top and bottom line up would give you a toroidal topology, not spherical. I assume your world is not doughnut shaped.

Normal cylindrical projections like this stretch out the poles from single points to lines as long as the equator. All the parallels in between also get stretched to the same length. So you get a varying amount of east-west stretch as you move north and south. In this particular projection there's no corresponding variation in north-south stretch. You need to draw that varying east-west stretching into your map or it won't look right when reprojected.